Is using phone with android/ipone as hotspot safe?

What am I asking here are privacy issues, not security.
When I search web using the internet given from wi-fi on phone, my ISP see what I am looking. But what about phone provider (google/apple). Do they know the same data (more/less) like ISP?

I am not asking what is going on when you search web on mobile phone (it may be another topic), but when you use phone as hotspot for e.g. laptop.

Ill try to answer your question as how I can understand it.

Privacy-wise the ISP can see what the sites you are connecting to. The client connection will still be seen by the ISP. This can be solved by the hotspot connecting to a VPN server prior to allowing others to connect.

On the side of the client connection. If the app has the priviledge to connect to the hotspot. It should be able to see the hotspot name. The hostpot name could eventually be seen in sites like Shodan if the client device is compromised. Not sure what else can leak through.